Rachel's Coffee Shop makes a blend that is a mixture of two types of coffee. Type A coffee costs Rachel $4.20 per pound, and typ
e B coffee costs $5.50 per pound. This month's blend used four times as many pounds of type B coffee as type A, for a total cost of $864.60. How many pounds of type A coffee were used?
Let's call the use the variables A and B to represent the number of pounds used for those types of coffee and set up a system of equations below to solve.
4.20A+5.50B=864.60
B=4A
Let's replace B in the first equation with 4A.
4.20A+5.50(4A)=864.60
Undo the parentheses.
4.20A+22A=864.60
Combine like terms.
26.2A=864.6
Divide both sides by 26.2
A=33
Therefore 33 pounds of type A coffee were used in this month's blend at Rachel's Coffee Shop.
